github.com/graybobo/golang.org-package-offline-cache@v0.0.0-20200626051047-6608995c132f/x/crypto/bn256/constants.go (about)

     1  // Copyright 2012 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package bn256
     6  
     7  import (
     8  	"math/big"
     9  )
    10  
    11  func bigFromBase10(s string) *big.Int {
    12  	n, _ := new(big.Int).SetString(s, 10)
    13  	return n
    14  }
    15  
    16  // u is the BN parameter that determines the prime: 1868033³.
    17  var u = bigFromBase10("6518589491078791937")
    18  
    19  // p is a prime over which we form a basic field: 36u⁴+36u³+24u³+6u+1.
    20  var p = bigFromBase10("65000549695646603732796438742359905742825358107623003571877145026864184071783")
    21  
    22  // Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u³+6u+1.
    23  var Order = bigFromBase10("65000549695646603732796438742359905742570406053903786389881062969044166799969")
    24  
    25  // xiToPMinus1Over6 is ξ^((p-1)/6) where ξ = i+3.
    26  var xiToPMinus1Over6 = &gfP2{bigFromBase10("8669379979083712429711189836753509758585994370025260553045152614783263110636"), bigFromBase10("19998038925833620163537568958541907098007303196759855091367510456613536016040")}
    27  
    28  // xiToPMinus1Over3 is ξ^((p-1)/3) where ξ = i+3.
    29  var xiToPMinus1Over3 = &gfP2{bigFromBase10("26098034838977895781559542626833399156321265654106457577426020397262786167059"), bigFromBase10("15931493369629630809226283458085260090334794394361662678240713231519278691715")}
    30  
    31  // xiToPMinus1Over2 is ξ^((p-1)/2) where ξ = i+3.
    32  var xiToPMinus1Over2 = &gfP2{bigFromBase10("50997318142241922852281555961173165965672272825141804376761836765206060036244"), bigFromBase10("38665955945962842195025998234511023902832543644254935982879660597356748036009")}
    33  
    34  // xiToPSquaredMinus1Over3 is ξ^((p²-1)/3) where ξ = i+3.
    35  var xiToPSquaredMinus1Over3 = bigFromBase10("65000549695646603727810655408050771481677621702948236658134783353303381437752")
    36  
    37  // xiTo2PSquaredMinus2Over3 is ξ^((2p²-2)/3) where ξ = i+3 (a cubic root of unity, mod p).
    38  var xiTo2PSquaredMinus2Over3 = bigFromBase10("4985783334309134261147736404674766913742361673560802634030")
    39  
    40  // xiToPSquaredMinus1Over6 is ξ^((1p²-1)/6) where ξ = i+3 (a cubic root of -1, mod p).
    41  var xiToPSquaredMinus1Over6 = bigFromBase10("65000549695646603727810655408050771481677621702948236658134783353303381437753")
    42  
    43  // xiTo2PMinus2Over3 is ξ^((2p-2)/3) where ξ = i+3.
    44  var xiTo2PMinus2Over3 = &gfP2{bigFromBase10("19885131339612776214803633203834694332692106372356013117629940868870585019582"), bigFromBase10("21645619881471562101905880913352894726728173167203616652430647841922248593627")}